Solve the system or linear equations

37. {-1, -1}.

Step-by-step explanation:

I'll solve the first one . The other can be solved in a similar way. We can use the method of elimination.

x1 - x2 = 0

3x1 - 2x2 = -1

We can multiply the first equation by -2. We then have an equation containing + 2x2 so when we add this to the second equation the 2x2 will be eliminated

So the first equation becomes:

-2x1 + 2x2 = 0     Bring down the second equation:

3x1 - 2x2 = -1       Now adding, we get:

x1 + 0 = -1

so x1 = -1.

Now we substitute this value of x1 in the original first equation:

-1 - x2 = 0

-1 = x2

x2 = -1.

So the solution set is {-1, -1}.

If there are more than 2 equations you can use a combination of substitutions and eliminations.

x= 17 cm

Step-by-step explanation:

Apply the Pythagorean relationship in this question which is stated mathematically as;

a² + b²= c²

where

a= is the base length, b is the height and c is the hypotenuse

First find length BC , where b= 8 cm and c=10cm and a=?

Hence;

a² + b²=c²

a² + 8²=10²

a²= 10²-8²

a²=100-64 =36

a=√36 = 6 cm

Now find AD=x where  AB=8cm , BD = 6+9= 15cm

In this case, a=15 cm , b=8cm , c=?

a² + b²=c²

15² + 8² = c²

225 + 64 = c²

289= c²

√289 = c

17 cm = c = x